Question

question
the graph of a line goes through the points (-4, 6) and (6, 1). what is the equation of the line in slope - intercept form?
enter the correct answer in the box by replacing m and b with the appropriate values.

(y = mx + b)

Explanation:

Step1: Find the slope \( m \)

The formula for slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Let \( (x_1, y_1)=(-4,5) \) and \( (x_2, y_2)=(6,1) \). Then \( m=\frac{1 - 5}{6 - (-4)}=\frac{-4}{10}=-\frac{2}{5} \).

Step2: Find the y - intercept \( b \)

Use the slope - intercept form \( y = mx + b \) and one of the points, say \( (6,1) \). Substitute \( x = 6 \), \( y = 1 \), and \( m=-\frac{2}{5} \) into the equation:
\( 1=-\frac{2}{5}(6)+b \)
\( 1=-\frac{12}{5}+b \)
To solve for \( b \), add \( \frac{12}{5} \) to both sides:
\( b = 1+\frac{12}{5}=\frac{5 + 12}{5}=\frac{17}{5}=3.4 \)
Now, the equation of the line in slope - intercept form is \( y=-\frac{2}{5}x+\frac{17}{5} \) (or \( y = - 0.4x+3.4 \)).

Answer:

\( y = -\frac{2}{5}x+\frac{17}{5} \) (or \( y=-0.4x + 3.4 \))